Is the salary considered unlawful if the employee finds no work to do due to a lack of assigned tasks, or due to his refusal of tasks outside his specialization and physical capacity?

If the contract stipulates the design of advertisements, then you are not obligated to perform any other work, and you are entitled to the full wage even if you are not assigned any work, because you are a private employee. However, if the contract stipulates working on the computer generally, then the requested work falls within the scope of the contract and you are obligated to fulfill it. If you are unable to do so, they have the right to terminate the contract. The reference for this is the saying of Allah the Almighty: (O you who have believed, fulfill [all] contracts), and the saying of the Prophet, peace and blessings be upon him: "Muslims are bound by their conditions concerning what is permissible."